In this section, we develop an algorithm to solve the Skillearn problem in Eq.(REF ), inspired by the algorithm in [1]}. For each learning stage \(k\)  with an optimization problem: \(\mathcal {W}_{k}^*(\lbrace \mathcal {U}_{j}\rbrace _{j=1}^k)=\textrm {min}_{\mathcal {W}_{k}} L_k(\mathcal {W}_{k},\mathcal {U}_{k},\lbrace \mathcal {W}_{j}^*(\lbrace \mathcal {U}_{i}\rbrace _{i=1}^{j})\rbrace _{j=1}^{k-1},\mathcal {D}^{(\textrm {tr})}_{k},\mathcal {F}_{k})+\gamma _k I_k(\mathcal {W}_{k},\mathcal {U}_{k},\lbrace \mathcal {W}_{j}^*(\lbrace \mathcal {U}_{i}\rbrace _{i=1}^{j})\rbrace _{j=1}^{k-1},\mathcal {F}_k)\) , we approximate the optimal solution \(\mathcal {W}_{k}^*(\lbrace \mathcal {U}_{j}\rbrace _{j=1}^k)\)  by one-step gradient descent update of the variable \(\mathcal {W}_{k}\) :
\(\begin{array}{l}\mathcal {W}_{k}^*(\lbrace \mathcal {U}_{j}\rbrace _{j=1}^k)\approx \mathcal {W}^{\prime }_{k}(\lbrace \mathcal {U}_{j}\rbrace _{j=1}^k)=\\\mathcal {W}_{k}-\eta \nabla _{\mathcal {W}_{k}}(L_k(\mathcal {W}_{k},\mathcal {U}_{k},\lbrace \mathcal {W}_{j}^*(\lbrace \mathcal {U}_{i}\rbrace _{i=1}^{j})\rbrace _{j=1}^{k-1},\mathcal {D}^{(\textrm {tr})}_{k},\mathcal {F}_{k})+\gamma _k I_k(\mathcal {W}_{k},\mathcal {U}_{k},\lbrace \mathcal {W}_{j}^*(\lbrace \mathcal {U}_{i}\rbrace _{i=1}^{j})\rbrace _{j=1}^{k-1},\mathcal {F}_k)).\end{array}\) 
